By my count, there are five different ways to think about the relation of God and truth:
1) There is truth, but there is no God.
2) There is truth, and there is God, but God is not the ontological ground of truth.
3) There is truth, there is God, and truth ultimately depends on the existence of God. There is truth only because there is God.
4) There is no truth, because there is no God.
5) There is God, but no truth.
Ad (1). This I would guess is the view of many if not most today. There are truths, and among these truths is the truth that God does not exist. This, I take it, is the standard atheist view.
Ad (2). This, I take it, would be the standard theist view among analytic philosophers. Consider a philosopher who holds that God is a necessary being and also holds that it is necessarily the case that there are some truths, but would deny the truth of the subjunctive conditional, If, per impossibile, God were not to exist, then truths would not exist either.
Ad (3). This is the view that I am inclined to accept. Thus I would affirm the subjunctive conditional lately mentioned. The difference between (2) and (3) is subtle. On both sides it is held that both God and truths are necessary, but the Augustinian — to give him a name — holds that God is the ultimate 'source' of all truth and thus of all intelligibility, or, if you prefer, the ultimate 'ground' of all truth and intelligibility.
Ad (4). This is Nietzsche's view. Tod Gottes = Tod der Wahrheit.
Ad (5). I have the impression that certain post-Nietzschean POMO-heads hold this. It is a view not worth discussing.
I should think only the first three views have any merit.
Each of the three has difficulties and none of the three can be strictly proven.
I will mention quickly a problem for the admittedly plausible first view.
Among the truths there are necessary truths such as the laws of logic. Now a truth is a true truth-bearer, a true proposition, say. Nothing can have a property unless it exists. (Call this principle Anti-Meinong). So no proposition can have the property of being true unless the proposition exists. A necessary truth is true in every metaphysically possible world. It follows that a necessarily true proposition exists in every possible world including worlds in which there are no finite minds. But a proposition is a thought-accusative that cannot exist except in, or for, a mind. If there is no God, or rather, if there is no necessarily existent mind, every mind is contingent. A contradiction ensues: there is a world W such that, in W, there exists a thought-accusative that is not the thought-accusative of any mind.
Here are some ways an atheist might 'solve' the problem:
a) Deny that there are necessary truths.
b) Deny that truth is any sense a property of propositions.
c) Deny Anti-Meinong.
d) Deny that propositions are thought-accusatives; accept some sort of Platonism about propositions.
But each of these denials involves problems of its own which I would have no trouble unpacking.
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